Zonked female cat at spay and neuter clinic - Photo by Average Jane (Flickr)
Low cost spay and neuter clinics provide a wonderful service because a lot of people who keep cats will resist spending money on veterinarian bills in these difficult times (2011). That said it is actually very cost effective to spay (for females) or neuter (castration in males) your cat for the obvious reasons that it avoids unwanted litters and it modifies the cat's behaviour in a way that saves money.
For example the male cat once neutered is less likely to spray urine to mark territory (and that might be in the home) and becomes less territorial so less likely to get into fights and therefore less money is spent on patching him up at the vet with injuries that cause abscesses for example. Neutering a male prevents testicular cancer although to be honest I am not sure that that is a major benefit because I don't think testicular cancer is that commonplace.
For the female cat the benefit is that it prevents uterine infections and breast cancer.
The big benefit to spaying and neutering is to the community of both people and cats. Overproduction of cats leads to more abandonments of cats and more stray and feral cats. These cats lead generally unhappy and often unhealthy lives under difficult conditions and it irritates a lot of people some of whom want to harm the cats. Many people help feral cats however. But the better course of action is taking proactive, preventative steps.
If I am honest (again) there some relatively minor downsides to neutering a male cat. If done early and it often is he will lose some of that attractive (to some people) maleness in appearance. I mean the jowly solid look. If castration is carried out before 6 months of age his penis can remain small. This is another indicator of how castration can affect a male cat's physical appearance.
And for both male and females spaying and neutering can lead to putting on weight despite the fact that the ASPCA says it does not. It might not cause weight gain but it might in some individual cats.
Another obvious downside is that female spaying is carried out under general anaesthetic. There is a risk of fatality under general anaesthetic. The risk seems to vary between 0.1 and 1% (see anaesthesia and cats).
Anyway the bottom line is that we have to spay and neuter our cats for the general good. I think most people would agree that. Low cost spay and neuter clinics allow people on low incomes to avail themselves of the services of veterinarians. It is probable that the poorer sections of society are more likely to not fix their cats so these clinics are important to society.
Where the low cost spay and neuter clinics?
In the USA, ASPA have an interactive, customised Google map - really nice. This is the page to go to. The link opens a new tab or window on your browser.
In the UK, the Cat Chat website has a list.
As to the rest of Europe I could not find details - sorry but you might like to read the ultimate guide to financial aid for pets.